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Proof step 210 from proof inv-rename-dir-negdentry (previous step)

(m = m9 ⊃ mkdir(m1, md, # links(m9, dirs0), m2, entries0 -- str);mkdir(m19, md8, # links(m, dirs0), m21, entries6)) = mkdir(m4, md3, m6, m7, entries2), (m9 = m ⊃ mkdir(m4 + 1, md4, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md0, # links(m9, dirs0), m2, entries0 -- str)) = mkdir(m0, md1, m11, m12, entries1), (m = m9 ⊃ mkdir(m4 + 1, md0, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]])) = mkdir(m13, md6, m14, m15, entries5), dirs0[entries0[str]] = mkdir(m3, md2, # links(entries0[str], dirs0), m5, entries), dirs0[m] = mkdir(m19, md8, # links(m, dirs0), m21, entries6), dirs0[m9] = mkdir(m1 + 1, md, # links(m9, dirs0), m2 + 1, entries0), afs-cons(dirs0, files), afs-cons (dirs0 [m9, (m9 = m ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m9, dirs0), m2, entries0 -- str)).meta:= md0 ] [m, mkdir(m13, md4, m14, m15, entries5) ], files), synced(dirs0, icache0, pcache), entries0[str] ∈ dirs0, str ∈ entries0, m9 ∈ dirs0, m ∈ dirs0, m = m9 → md4 = md0, asynced2 → synced(files, icache0, pcache), dentrykey(m, str0) ∈ dcache0 → str0 = dcache0[dentrykey(m, str0)].name ∧ (dcache0[dentrykey(m, str0)].ino ∈ dirs0 ∨ dcache0[dentrykey(m, str0)].ino ∈ files) ∧ dcache0[dentrykey(m, str0)].name ∈ entries6 ∧ dcache0[dentrykey(m, str0)].ino = entries6[dcache0[dentrykey(m, str0)].name] ∧ dcache0[dentrykey(m, str0)].dentry?, ∀ key0. key0 ∈ dcache0 → key0.dentry? ∧ key0.name = dcache0[key0].name ∧ key0.ino ∈ dirs0 ∧ (links(key0.ino, dirs0) ≠ ∅ ∨ key0.ino = ROOT_INO) ∧ (dcache0[key0].ino ∈ dirs0 ∨ dcache0[key0].ino ∈ files) ∧ dcache0[key0].name ∈ dirs0[key0.ino].entries ∧ dcache0[key0].ino = dirs0[key0.ino].entries[dcache0[key0].name] ∧ dcache0[key0].dentry?, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m9, dirs0) ≠ ∅ ∨ m9 = ROOT_INO ⊦ str0 ∈ entries6, ( links (m, dirs0 [m9, (m9 = m ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m9, dirs0), m2, entries0 -- str)) .meta:= md0 ] [m, mkdir(m13, md4, m14, m15, entries5) ]) ≠ ∅ ∨ m = ROOT_INO) ∧ str0 ∈ entries5 ∧ entries0[str] = entries5[str0]

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 211:
(m = m9 ⊃ mkdir(m4 + 1, md0, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]])) = mkdir(m13, md6, m14, m15, entries5), (m9 = m ⊃ mkdir(m4 + 1, md4, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md0, # links(m9, dirs0), m2, entries0 -- str)) = mkdir(m0, md1, m11, m12, entries1), (m = m9 ⊃ mkdir(m1, md, # links(m9, dirs0), m2, entries0 -- str);mkdir(m19, md8, # links(m, dirs0), m21, entries6)) = mkdir(m4, md3, m6, m7, entries2), dirs0[m9] = mkdir(m1 + 1, md, # links(m9, dirs0), m2 + 1, entries0), dirs0[m] = mkdir(m19, md8, # links(m, dirs0), m21, entries6), dirs0[entries0[str]] = mkdir(m3, md2, # links(entries0[str], dirs0), m5, entries), m = m9, afs-cons (dirs0 [m9, (m9 = m ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m9, dirs0), m2, entries0 -- str)).meta:= md0 ] [m, mkdir(m13, md4, m14, m15, entries5) ], files), afs-cons(dirs0, files), synced(dirs0, icache0, pcache), m ∈ dirs0, m9 ∈ dirs0, str ∈ entries0, entries0[str] ∈ dirs0, dentrykey(m, str0) ∈ dcache0 → str0 = dcache0[dentrykey(m, str0)].name ∧ (dcache0[dentrykey(m, str0)].ino ∈ dirs0 ∨ dcache0[dentrykey(m, str0)].ino ∈ files) ∧ dcache0[dentrykey(m, str0)].name ∈ entries6 ∧ dcache0[dentrykey(m, str0)].ino = entries6[dcache0[dentrykey(m, str0)].name] ∧ dcache0[dentrykey(m, str0)].dentry?, asynced2 → synced(files, icache0, pcache), m = m9 → md4 = md0, ∀ key0. key0 ∈ dcache0 → key0.dentry? ∧ key0.name = dcache0[key0].name ∧ key0.ino ∈ dirs0 ∧ (links(key0.ino, dirs0) ≠ ∅ ∨ key0.ino = ROOT_INO) ∧ (dcache0[key0].ino ∈ dirs0 ∨ dcache0[key0].ino ∈ files) ∧ dcache0[key0].name ∈ dirs0[key0.ino].entries ∧ dcache0[key0].ino = dirs0[key0.ino].entries[dcache0[key0].name] ∧ dcache0[key0].dentry?, links(m9, dirs0) ≠ ∅ ∨ m9 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ str0 ∈ entries6, ( links (m, dirs0 [m9, (m9 = m ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m9, dirs0), m2, entries0 -- str)) .meta:= md0 ] [m, mkdir(m13, md4, m14, m15, entries5) ]) ≠ ∅ ∨ m = ROOT_INO) ∧ str0 ∈ entries5 ∧ entries0[str] = entries5[str0]

Rule argument

fma: m = m9

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)%⊦ mkdir(m, md, m0, m1, entries).meta:= md0 = mkdir(m, md0, m0, m1, entries); (s)% ⊦ str ∈ entries[str, ino]; (s)% ⊦ entries[str, ino][str] = ino; (s)%⊦ afs-cons(dirs, files) → ( links(ino, dirs) = ∅ ↔ (ino ∈ dirs → dirs[ino].nlink = 0) ∧ (ino ∈ files → files[ino].nlink = 0)); (ws)% ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s)% ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s)% ⊦ mkdir(m, md, m0, m1, entries).nlink = m0; (s)% ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (s)%size-zero-02: ⊦ # ls = 0 → ls = ∅; (forward) from specification set-basic[alink-set]%size-zero-01: ⊦ ls ≠ ∅ → # ls ≠ 0; (forward) from specification set-basic[alink-set]%afs-cons-dir-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) → # links(ino, dirs) = n; (forward) from specification afs-base Used formulas: m = m9